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- W2316183734 startingPage "1029" @default.
- W2316183734 abstract "In this paper, we study the nonlinear wave solutions of thegeneralized $b$-equation involving two parameters $b$ and $k$. Let$c$ be constant wave speed, $c_5=$$frac{1}{2}(1+b-sqrt{(1+b)(1+b-8k)})$,$c_6=frac{1}{2}(1+b+sqrt{(1+b)(1+b-8k)})$. We obtainthe following results: 1. If $-infty 2. If $-infty 3. If $k=frac{1+b}{8}$ and $c=frac{b+1}{2}$, then there aretwo types of explicit nonlinear wave solutions, fractionalpeakon wave solution and fractional blow-up solution.Not only is the existence of these solutions shown, but theirconcrete expressions are presented. We also reveal the relationships amongthese solutions. Besides, the correctness of these solutionsis tested by using the software Mathematica." @default.
- W2316183734 created "2016-06-24" @default.
- W2316183734 creator A5047101056 @default.
- W2316183734 date "2012-09-01" @default.
- W2316183734 modified "2023-10-18" @default.
- W2316183734 title "The explicit nonlinear wave solutions of the generalized $b$-equation" @default.
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- W2316183734 doi "https://doi.org/10.3934/cpaa.2013.12.1029" @default.
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